Aug. 15, 1925 
Coefficients of Inbreeding and Relationship 
383 
not, of course, give the probable error of the change in percentage of 
homozygosis. This is a function of the unknown number of Men- 
delian factors which were heterozygous in the foundation stock. The 
complete coefficient should give the decrease in heterozygosis very 
accurately for characters dependent on thousands of genes but with 
very little reliability in an individual case for a character dependent 
on only two or three genes. 
RELATIONSHIP 
The calculation of coefficients of relationship from random samples 
of pedigrees offers no additional complications of importance. 
The presence of a tie between single random lines back of the two 
1 +F a 
animals considered ( X , Y) indicates a coefficient of _ . 
y(l + F x ) (l + /v 
A tie in a comparison of four-column pedigrees (four possible ties) 
t l R “I 
ij== ■ to the coefficient, and similarly for 
V(i + /v (1 + *VJ 
larger pedigrees. In calculating the relationship of a large group to a > 
particular animal (Y), the coefficient of inbreeding of that animal 
( F y ) should of course be obtained with a high degree of reliability. 
The coefficient (F a ) of common ancestors that frequently recur should 
be calculated with considerable reliability. The coefficient (F x ) 
for the animals of the group should be calculated once for all, prefer¬ 
ably by the two-column method. 
In this case, the denominator becomes a constant factor, and only 
the numerator varies for different ties. The reader will have no 
difficulty in extending the method to other sorts of cases, such as 
finding the correlation between random individuals of the breed, 
or within a specially choice section of the breed, or between two 
sections of the breed. The probable error can be calculated from the 
proportion of ties, and be rated up by the ratio of the coefficient 
to this proportion as in the case of tne inbreeding coefficient. 
The writers have made a number of tests of the reliability of the 
method. The average coefficient of inbreeding of the 64 Bates 
Duchesses, calculated from the complete pedigrees, was given as 
40.9 per cent. The random method, using four-column pedigrees, 
gave 42.2 per cent with a probable error of 1.1 per cent. The ob¬ 
served difference (1.3 per cent) happens to be slightly greater than 
the probable error. It is evident that the enormously simpler 
approximate method gives a sufficiently accurate measure of the 
average inbreeding of the Duchesses as a group. 
As an example of the application of the method to the inbreeding 
of an individual, it was found that 1,024 wholly random two-column 
samples of the pedigree of Favourite (252) gave a coefficient of 
19.0 ±0.52 per cent. The complete method gives 19.2 per cent. 
